A fully nonlinear solution of the flow around a spinning spheroid in a rotating stratified fluid

This paper investigates the flow and density field around a spinning solid spheroid with a given aspect ratio, immersed in a rotating stratified fluid. First, we derive the general system of equations governing such flows around any solid of revolution in the limit of infinite Schmidt number. We then present an exact analytical solution for a spinning spheroid of arbitrary aspect ratio. For the specific case of a sphere, we provide the diffusive spin-up solution obtained via an inverse Laplace integral. To validate the theoretical results, we experimentally reproduce these flows by spinning spheroids in a rotating tank filled with stratified salt water. By varying the stratification intensity, the angular velocities of the spheroid and the rotating table, and the spheroid’s shape, we explore a broad parameter space defined by Froude, Reynolds and Rossby numbers and aspect ratio. Using particle image velocimetry to measure the velocity field, we demonstrate excellent agreement between theory and experiments across all tested regimes.